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Dynamical Meteorology in the Tropics: Asymptotic Nondivergence?

Dynamical Meteorology in the Tropics: Asymptotic Nondivergence?. by Jun-Ichi Yano with M. Bonazzola, S. Mulet, K. Delayen, S. Hagos, C. Zhang, D. Netherly. Large-Scale Tropical Tropsopheric Dynamics:. Vorticity is dominant more than Divergence.

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Dynamical Meteorology in the Tropics: Asymptotic Nondivergence?

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  1. Dynamical Meteorology in the Tropics: Asymptotic Nondivergence? by Jun-Ichi Yano with M. Bonazzola, S. Mulet, K. Delayen, S. Hagos, C. Zhang, D. Netherly

  2. Large-Scale Tropical Tropsopheric Dynamics: • Vorticity is dominant more than Divergence • Deep Convection is secondary, and can be treated as a “catalytic” perturbation effect • Strongly Nonlinear

  3. Large-Scale Tropical Tropsopheric Dynamics: • Vorticity is dominant more than Divergence • Deep Convection is secondary, and can be treated as a “catalytic” perturbation effect • Strongly Nonlinear

  4. Scale Analysis (Charney 1963) • L~1000km, U~10m/s: vorticity>>divergence i.e., nondiverget to the leading order orasymtotically nondivergent • cf., L~3000km, U~3m/s: • Linear Equatorial Waves • (cf., Yano and Bonazzola, 2009, JAS)

  5. vorticity>>divergence ?

  6. 850hPa Scatter Plots between Vorticity and Divergence: TOGA-COARE LSA Data divergence vorticity 500hPa divergence vorticity (cf., Yano, Multet, and Bonazzola, 2009, Tellus) 250hPa divergence vorticity

  7. Measure of a Variability (RMS of a Moving Average): where

  8. horizontal scale (km) Time scale (days) RMS of Divergence/Vorticity (Transient)

  9. OLR Spectrum: Dry Equatorial Waves with hE=25 m (Wheeler & Kiladis 1999) Equatorially asymmetric Equatorially symmetric Frequency Frequency Zonal Wavenumber Zonal Wavenumber

  10. Is this observational diagnosis consistent with (convectively-coupled) linear equatorial wave theories? (cf., Delayen and Yano, 2009, Tellus)

  11. Linear Free Wave Solutions: RMS of divergence/vorticity cg=50m/s cg=12m/s

  12. Linear Forced Wave Solutions(cg=50m/s): RMS of divergence/vorticity n=0 n=1

  13. Asymptotically Nondivergent but Asymptotic Nondivergence is much weaker than those expected from linear wave theories (free and forced) Nonlinearity defines the divergence/vorticity ratio (Strongly Nonlinear)

  14. Asymptotically Nondivergent Dynamics (Formulation): • Leading-Order Dynamics: • Conservation of Absolute Vorticity • Higher-Order: • Perturbation“Catalytic” Effect of Deep Convection • Slow Modulation of the Amplitude of the Vorticity

  15. Asymptotically Nondivergent Dynamics (Formulation): • Leading-Order Dynamics: • Conservation of Absolute Vorticity: :Modon Solution?

  16. Is MJO a Modon?: Absolute Vorticity Streamfunction A snap shot from TOGA-COARE (Indian Ocean): 40-140E, 20S-20N ? (Yano, S. Hagos, C. Zhang)

  17. Conclusions: Large-Scale Tropical Tropsopheric Dynamics: • Asymptotically Nondivergent • Asymptotic Nondivergence is much weaker than those expected from linear wave theories • (free and forced) Is MJO a Modon? • Strong Nonlinearty:

  18. Last Theorem “Asymptotic nondivergence” is equivalent to “Longwave approximation” to the linear limit. (man. rejected by Tellus 2010, JAS 2011) Last Question: What is wrong with this theorem? Last Remark However, “Asymptotic nondivergence” provides a qualitatively different dynamical regime under Strong Nonlinearity. Reference: Wedi and Smarkowiscz (2010, JAS)

  19. Balanced Dynamics (Asymptotic: Charney) Q=Q(q, q,… ) Qw • divergence equation (diagnostic) f barotropics b-plane vorticity equation Rossby waves (without geostrophy): vH(0) } • hydrostatic balance: f q • continuity: w weak divergence weak forcing on vorticity (slow time-scale) • thermodynamic balance: w~Q: • dynamic balance: non-divergent • vorticity equation (prognostic) • moisture equation (prognostic): q

  20. Scale Analysis (Summary) (Simple) (Asymptotic) R.2. Vertical Advection: • L~3000km, U~3m/s (cf., Gill 1980): • Wave Dynamics (Linear) • L~1000km, U~10m/s (Charney 1963): • Balanced Dynamics (Nonlinear) R.1. Nondimensional: b =2WL2/aU

  21. Scale Analysis (Charney 1963) Thermodynamic equaton: i.e., the vertical velocity vanishes to leading order i.e., the horizontal divergence vanishes to leading order of asymptotic expansion i.e., Asymptotic Nondivergence

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